Problem: Simplify the following expression: $r = \dfrac{a^2 - 4a + 3}{a - 1} $
Explanation: First factor the polynomial in the numerator. $ a^2 - 4a + 3 = (a - 1)(a - 3) $ So we can rewrite the expression as: $r = \dfrac{(a - 1)(a - 3)}{a - 1} $ We can divide the numerator and denominator by $(a - 1)$ on condition that $a \neq 1$ Therefore $r = a - 3; a \neq 1$